A year ago I traded my 2012 Ford Focus for a 2014 Subaru Outback 2.5i Premium (automatic transmission). Dealer told me it could be flat towed, made sense to me, why not so long as it is in neutral? Well, found out that is not the case of course. Very irritating given that my Focus COULD be flat towed.

My question, would there be any issue with flat towing my Subaru behind my RV if I had the engine running in the Subaru with the transmission in neutral? Other than wasting gas and racking up miles on the odometer, is there any real problem with this idea?

Also was not certain how this might affect wiring the Subaru's lights with the RV's lights since the power would be on in the Subaru. Would external lights need to be used instead?

If your dealer told you it could be flat towed and it can't, take it back and demand a full refund under whatever local legislation you have which mirrors the UK sale of goods act with reference to misrepresentation. It's not up to you to try and come up with a solution when you checked prior to purchase and were misinformed. Failing that, have the dealership buy you a trailer.
– Steve MatthewsJun 10 '16 at 10:44

... the information in the Outback owners manual being vague when it comes to recreational towing. It specifically says not to tow automatic and CVT vehicles faster than 20 mph and for no more than 31 miles.

In a subsequent post in the same thread, it was further answered about manual transmission Outbacks having the ability to flat tow:

AWD Subaru vehicles with manual transmission can be towed with all four wheels on the ground and the transmission in neutral. When towing a manual transmission Subaru behind your motor home, you would want the transmission in neutral and the key in the 'ACC' position. As all new models are equipped with digital odometers, mileage will not accumulate when being towed.

If you are going to tow an AWD Outback (which I assume most of them are AWD) for any extended period of time, you need to have them on a trailer. This would seriously be your best option if you are going to be towing it a lot. Consider the trade off in the mileage, fuel, piece-of-mind against the purchase price of the trailer. I've looked into towed vehicle trailers and have found them quite reasonable. You'd recoup the cost in no time, especially if your found a decent used one.

Would there be any issue with flat towing my Subaru behind my RV if I had the engine running in the Subaru with the transmission in neutral? Other than wasting gas and racking up miles on the odometer, is there any real problem with this idea?

I think you are on the right track here. It would provide lubricant to vital transmission parts to do this while pulling it ... but why would you? It sounds like a recipe for disaster if you ask me. If the Outback were to run out of fuel for some stupid reason, you'd destroy the transmission/transfer in it. If you left it running/attached and went in to go to the bathroom somewhere, you'd come out and find the car gone because someone took it (I guess if you have a key fob, you could lock/unlock the vehicle). I don't know, there is just something inherently wrong with doing this.

Would external lights need to be used instead?

This would be your best bet. You can get light bars like tow trucks use. They come with LEDs which are much better than incandescent, with magnets which hold them to the roof of the towed vehicle. This would avoid you having to hack the wiring harness. I'm sure you could wire the turn indicators like you would do regularly with a flat towed vehicle without issue, even if it were running. I take it you have experience in this arena, so would leave the particulars up to you.

You can tow any vehicle with a manual transmission, including subaru, with the transmission in neutral.
– SoilSciGuyJul 14 '18 at 16:11

@SoilSciGuy - Actually you shouldn't flat tow a Subaru. It's not the transmission you are worried about, but the transfer and differentials, which are still cranking around whether the tranny is in neutral or not.
– Pᴀᴜʟsᴛᴇʀ2♦Jul 14 '18 at 16:58

Actually, it states in the user manual that it can be towed
– SoilSciGuyJul 14 '18 at 17:01

Differentials don't have oil pumps, automatic transmissions do and oil does not circulate in an automatic unless the oil pump is running with the engine on.. Subaru in the US does not have a transfer case, and I've never heard of a transfer case that can't be placed in neutral.
– SoilSciGuyJul 14 '18 at 17:07